Knowing the truth is rarely enough -- we also seek out reasons why the fact is true. While much is known about how we explain contingent truths, we understand less about how we explain facts, such as those in mathematics, that are true as a matter of logical necessity. We present a framework, based in computational complexity, where explanations for deductive truths co-emerge with discoveries of simplifying steps during the search process. When such structures are missing, we revert, in turn, to error-based reasons, where a (corrected) mistake can serve as fictitious, but explanatory, contingency-cause: not making the mistake serves as a reason why the truth takes the form it does. We simulate human subjects, using GPT-4o, presented with SAT puzzles of varying complexity and reasonableness, validating our theory and showing how its predictions can be tested in future human studies.

The field of AI (artificial intelligence), to those on the outside, must appear to be an orderly gathering of intellectuals collaborating at the cutting edge of technology. The reality is a bit different. Last year, Elon Musk made headlines by describing AI as a "fundamental risk to the existence of civilization." More recently, Google CEO Eric Schmidt suggested that the answer to fears about AI was to police it and offered the example of finding a way to police the misuse of the telephone because of its possible misuse by some individuals with bad intentions rather than not inventing the phone at all. One of the biggest misconceptions surrounding AI is that most individuals think that humanity is close to it, although in fact the reality is quite different. Although a great deal has been learned about how to engineer certain narrow problems like speech recognition in ways which could not have been imagined five or ten years ago, the idea of having machines that can reason about the world in the ways that human-beings can is still implausible.

Truly revolutionary political transformations are naturally of great interest to historians, and the French Revolution at the end of the 18th century is widely regarded as one of the most influential, serving as a model for building other European democracies. A paper published last summer in the Proceedings of the National Academy of Sciences, offers new insight into how the members of the first National Constituent Assembly hammered out the details of this new type of governance. Specifically, rhetorical innovations by key influential figures (like Robespierre) played a critical role in persuading others to accept what were, at the time, audacious principles of governance, according to co-author Simon DeDeo, a former physicist who now applies mathematical techniques to the study of historical and current cultural phenomena. And the cutting-edge machine learning methods he developed to reach that conclusion are now being employed by other scholars of history and literature. As more and more archives are digitized, scholars are applying various analytical tools to those rich datasets, such as Google N-gram, Bookworm, and WordNet.

Truly revolutionary political transformations are naturally of great interest to historians, and the French Revolution at the end of the 18th century is widely regarded as one of the most influential, serving as a model for building other European democracies. A paper published last summer in the Proceedings of the National Academy of Sciences, offers new insight into how the members of the first National Constituent Assembly hammered out the details of this new type of governance. Specifically, rhetorical innovations by key influential figures (like Robespierre) played a critical role in persuading others to accept what were, at the time, audacious principles of governance, according to co-author Simon DeDeo, a former physicist who now applies mathematical techniques to the study of historical and current cultural phenomena. And the cutting-edge machine learning methods he developed to reach that conclusion are now being employed by other scholars of history and literature. As more and more archives are digitized, scholars are applying various analytical tools to those rich datasets, such as Google N-gram, Bookworm, and WordNet.

The field of AI (artificial intelligence), to those on the outside, must appear to be an orderly gathering of intellectuals collaborating at the cutting edge of technology. The reality is a bit different. Last year, Elon Musk made headlines by describing AI as a "fundamental risk to the existence of civilization." More recently, Google CEO Eric Schmidt suggested that the answer to fears about AI was to police it and offered the example of finding a way to police the misuse of the telephone because of its possible misuse by some individuals with bad intentions rather than not inventing the phone at all. One of the biggest misconceptions surrounding AI is that most individuals think that humanity is close to it, although in fact the reality is quite different. Although a great deal has been learned about how to engineer certain narrow problems like speech recognition in ways which could not have been imagined five or ten years ago, the idea of having machines that can reason about the world in the ways that human-beings can is still implausible.

The field of artificial intelligence, to those on the outside, must appear to be an orderly gathering of intellectuals collaborating at the cutting edge of technology. If you dig beyond the hyperbole of Elon Musk and the wonders promised by Google, there's a number of gnashing dissenters who're happy to toss shade at the entire industry. These people are called academics. And, I'll be up front, I think they have a point. But more on that later, for now let's talk about Simon DeDeo.

Being a voracious reader is a prerequisite for academics in the humanities, but even the most dedicated bookworm needs to eat, sleep, and socialize. Not so for computers, which are known for being tireless, thorough, and very fast. And, when asked the right kinds of questions, these electronic speed-readers can grasp patterns that would otherwise lie beyond the reach of human scholars. That's exactly what happened when a team of researchers used machine-learning techniques to plow through transcripts of 40,000 speeches in a parliamentary assembly during the first two years of the French Revolution, according to a paper published in the Proceedings of the National Academy of Sciences last month. By quantifying the novelty of speech patterns and the extent to which those patterns were copied by subsequent speakers, the researchers illustrated how much of the important intellectual work of the revolution was initially carried out in committees, rather than in the whole assembly.

The French Revolution was one of the most important political transformations in history. Even today, more than 200 years later, it's held up as a model of democratic nation-building. But for years, historians and political scientists have wondered just how the democratic trailblazers of the French Revolution managed to pull off the creation of an entirely new kind of governance. New research from an interdisciplinary collaboration among historians, political scientists, and statisticians suggest that rhetorical innovations may have played a significant role in winning acceptance for the new principles of governance that built the French republic's foundation -- and inspired future democracies around the world. The study, published today in PNAS, used machine learning techniques to comb through transcripts of 40,000 speeches from the deliberations of the makeshift assembly formed during the revolution's early days to hash out the laws and institutions of the new government.

Using the mathematical language of information theory, Hoel and his collaborators claim to show that new causes--things that produce effects--can emerge at macroscopic scales. They say coarse-grained macroscopic states of a physical system (such as the psychological state of a brain) can have more causal power over the system's future than a more detailed, fine-grained description of the system possibly could. Just as codes reduce noise (and thus uncertainty) in transmitted data--Claude Shannon's 1948 insight that formed the bedrock of information theory--Hoel claims that macro states also reduce noise and uncertainty in a system's causal structure, strengthening causal relationships and making the system's behavior more deterministic. With Albantakis and Tononi, Hoel formalized a measure of causal power called "effective information," which indicates how effectively a particular state influences the future state of a system.